Question

According to the National Restaurant Association, 23% of fine-dining restaurants have instituted policies restricting the use of cell phones.

a. If you select a sample of 125 fine-dining restaurants, what is the probability that the sample has between 18% to 28% restaurants that have established policies restricting the use of cell phones?

b. If you select a sample of 125 fine-dining restaurants, compute the symmetrical limits within which the sample percentage will be contained 95% of the time.

Answer 1

first, we will find mean and standard deviation for the given data  

mean =

standard deviation =

(A) we have to find probability that the sample has between 18% to 28% restaurants.

using normalcdf

setting lower = 0.18, upper = 28, mean = 0.23 and sd = 0.038

we get

=normalcdf(lower, upper , mean,sd)

= normalcdf(0.18,0.28,0.23,0.038)

= 0.8159

(B) Using empirical rule, we know that 95% of the data falls within 2 standard deviation

so, required limits =